Our Mathematical Universe is a book by MIT physicist Max Tegmark. But a more appropriate title would be My Fantasies About Other Universes. Tegmark has long been a popularizer of the idea that our universe is only one of a huge or infinite set of universes called a multiverse. Tegmark distinguishes between 4 types of multiverses, which he calls Level I, Level II, Level III, and Level IV. Tegmark says he is a believer in a Level IV multiverse. He describes a Level IV multiverse as one consisting of a vast or infinite number of universes, each of which has a different mathematical structure. This is not science, but unverifiable metaphysics dressed up in scientific garb.
Tegmark gives some reasoning to support his belief in a Level IV multiverse, but it is not persuasive. He claims that a belief in a Level IV multiverse follows from the “mathematical universe hypothesis,” which he defines as the idea that “our external physical reality is a mathematical structure.” He defines a mathematical structure as “a set of abstract entities with relations between them.”
But this mathematical universe hypothesis is not a sound one. The universe is not a mathematical structure, because it is not a set of abstract entities. A mind can create various abstract entities when pondering the universe, but such abstract entities are not the same as the universe itself.
Consider a much simpler question: is our planet a mathematical structure? No, it is not. Our planet has the shape of a sphere, which is a mathematical structure. But our planet is vastly more than just a sphere, as a description of our planet would involve a vast number of details beyond that of a sphere. Just as it incorrect to say that our planet is a mathematical structure, it is incorrect to say that the universe itself is a mathematical structure.
Tegmark attempts to prove his mathematical universe hypothesis by arguing that it follows from an “external reality hypothesis,” which he defines as the hypothesis that there exists an external physical reality completely independent of us humans. But such a mathematical universe hypothesis in no way follows from such an external reality hypothesis, and Tegmark's reasoning that the one follows from the other is not at all convincing.
Tegmark gives an example of a chess match in an attempt to persuade us that everything can be reduced to a mathematical structure. He points out that we can reduce the chess match to an abstraction listing each piece and how it moved. But even this example fails. Even a chess match cannot be reduced to an abstract mathematical structure. To get the full story on what went on in a chess match, we must have not just the movement of the pieces, but the mind stream of the players: what exactly they were thinking at each point in the game, and what exactly they were feeling. There is no way to represent such streams of thought and feeling through an abstract mathematical representation. Even if one considers only physical things, you then have to consider that according to Heisenberg's uncertainty principle, all subatomic particles have a quantum fuzziness, meaning that they cannot be defined exactly in terms of both movement and position, unlike chess pieces on a chess board. You cannot even make a precise exact mathematical description of the arrangement of all the particles in your body.
Being something composed of almost infinitely diverse forms of matter that are widely separated, and also streams of experience and consciousness that cannot be mathematically represented, there is no mathematical structure that corresponds to the universe. Saying as Tegmark does that the universe is a mathematical structure is to make the same kind of mistake as saying that an office building is a blueprint or saying that an automobile is a 3D CAD model (or saying that a C++ object is a C++ class).
Tegmark has introduced the idea of the universe as a mathematical structure so that he can use the idea as a kind of a springboard to a multiverse theory. The idea has long been held that every type of mathematical structure exists in some eternal Platonic sense. For example, it has been held that there has eternally existed the idea of a triangle, the idea of a square, and so forth, going up to a figure with a countless number of sides. So Tegmark basically reasons that if our universe is a mathematical structure, and if every mathematical structure is real, then there must exist every imaginable universe that corresponds to each of the different possible mathematical structures. But this reasoning fails to persuade, simply because Tegmark fails to establish the unwarranted idea that our universe is a mathematical structure, an idea which has not received appreciable support from previous thinkers.
One can only ask: why does Max Tegmark have such an enthusiasm for multiverse theory? I think I have a possible explanation. Perhaps Tegmark wants to believe in many other universes because he thinks that our universe is very boring.
Why do I suggest that Tegmark thinks our universe is boring? Part of the reason is given in the last chapter of Tegmark's book. Tegmark argues that we are alone in our vast universe. He gives the same lame argument that has been advanced by Ray Kurzweil and others, the argument that if there were intelligent life elsewhere it would already have colonized our solar system. This argument has been rebutted successfully many times before, including in this post and this post. One reason the argument makes no sense is that intergalactic travel (involving distances of many thousands of light-years) is very probably impossible, and even interstellar travel is very probably extremely difficult (contrary to impressions given by science fiction such as Star Trek and Star Wars). Another reason the argument makes no sense is that there is no large nation on Earth which develops more than 95% of available territory (every large nation keeps a significant fraction of its available territory as undeveloped preserves or nature reserves). So there is no reason to assume that any race would go around colonizing every available planet or solar system.
The fact that we have found so many potentially habitable planets already contradicts Tegmark's thesis that we are alone in the universe, as does the fact that we live in a universe with at least 10,000,000,000,000,000,000 stars like the sun.
Credit: Planetary Habitability Laboratory, UPR Arecibo
Believing unwisely in the idea that man is the only intelligent species in the universe, Tegmark therefore believes in a dull desert of a universe, a universe with no beings more interesting than those we read about in our daily news. So we can make a guess as to why he is so attracted to speculations about other universes. It's rather like this. Imagine if you had only one sibling, a brother who was a real snooze, as dull as dishwater. You might be tempted to fantasize that you are adopted, and that you have unseen brothers you have never met, who live terribly exciting lives. But if your brother was an extremely interesting person with a fascinating life, you probably would not engage in such fantasies.
I think we live in a universe vastly more interesting than the very dull affair imagined by Tegmark. Contrary to what Tegmark claims, the evidence from astronomy actually suggests that the universe is teeming with intelligent life. We have every reason to suspect that the history of our universe is the most fascinating drama imaginable, a place where epics of evolution are being played out on trillions of civilized planets existing in billions of galaxies. We also have much evidence to suggest that the universe has a wide variety of fascinating paranormal phenomena which make it far more interesting than any materialist thinker can imagine.
How would you concisely describe such a universe, with such a staggering wealth of locations and phenomena, with such an incredible diversity of intelligent entities, some of which are protoplasmic, some of which may be electronic, and some of which may be purely spiritual? You might call it the most interesting universe imaginable. When you have that type of universe to study and ponder and investigate, why even bother with unverifiable speculations about other universes?